Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs

TLDR

Takagi–Sugeno fuzzy models and associated stability results are recalled. The paper introduces relaxed stability conditions and LMI‑based designs for continuous and discrete fuzzy control systems. The authors model nonlinear systems with Takagi–Sugeno fuzzy models, employ parallel distributed compensation, and develop relaxed stability conditions and LMI‑based design procedures—including additional LMIs for decay rate and input/output constraints—for fuzzy regulators and observers. Design examples confirm that the relaxed stability conditions and LMI‑based procedures effectively design fuzzy regulators and observers for nonlinear systems.

Abstract

This paper presents new relaxed stability conditions and LMI- (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. They are applied to design problems of fuzzy regulators and fuzzy observers. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy regulators and fuzzy observers, nonlinear systems are represented by Takagi-Sugeno's (TS) fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the TS fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers, LMI-based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions. Other LMI's with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures. Design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the LMI-based design procedures.